Solve for $x$ and $y$ using elimination. ${x-3y = -4}$ ${-4x+4y = -8}$
We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ ${4x-12y = -16}$ $-4x+4y = -8$ Add the top and bottom equations together. $-8y = -24$ $\dfrac{-8y}{{-8}} = \dfrac{-24}{{-8}}$ ${y = 3}$ Now that you know ${y = 3}$ , plug it back into $\thinspace {x-3y = -4}\thinspace$ to find $x$ ${x - 3}{(3)}{= -4}$ $x-9 = -4$ $x-9{+9} = -4{+9}$ ${x = 5}$ You can also plug ${y = 3}$ into $\thinspace {-4x+4y = -8}\thinspace$ and get the same answer for $x$ : ${-4x + 4}{(3)}{= -8}$ ${x = 5}$